Model-based Estimation of High Frequency Jump Diffusions with Microstructure Noise and Stochastic Volatility

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Abstract

When analysing the volatility related to high frequency financial data, mostly non-parametric approaches based on realised or bipower variation are applied. This article instead starts from a continuous time diffusion model and derives a parametric analog at high frequency for it, allowing simultaneously for microstructure effects, jumps, missing observations and stochastic volatility. Estimation of the model delivers measures of daily variation outperforming their non-parametric counterparts. Both with simulated and actual exchange rate data, the feasibility of this novel approach is shown. The parametric setting is used to estimate the intra-day trend in the Euro/U.S. Dollar exchange rate.